Ikabata Yasuhiro, Fujisawa Ryo, Seino Junji, Yoshikawa Takeshi, Nakai Hiromi
Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.
Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.
J Chem Phys. 2020 Nov 14;153(18):184108. doi: 10.1063/5.0021281.
The machine-learned electron correlation (ML-EC) model is a regression model in the form of a density functional that reproduces the correlation energy density based on wavefunction theory. In a previous study [T. Nudejima et al., J. Chem. Phys. 151, 024104 (2019)], the ML-EC model was constructed using the correlation energy density from all-electron calculations with basis sets including core polarization functions. In this study, we applied the frozen core approximation (FCA) to the correlation energy density to reduce the computational cost of the response variable used in machine learning. The coupled cluster singles, doubles, and perturbative triples [CCSD(T)] correlation energy density obtained from a grid-based energy density analysis was analyzed within FCA and correlation-consistent basis sets without core polarization functions. The complete basis set (CBS) limit of the correlation energy density was obtained using the extrapolation and composite schemes. The CCSD(T)/CBS correlation energy densities based on these schemes showed reasonable behavior, indicating its appropriateness as a response variable. As expected, the computational time was significantly reduced, especially for systems containing elements with a large number of inner-shell electrons. Based on the density-to-density relationship, a large number of data (5 662 500 points), which were accumulated from 30 molecules, were sufficient to construct the ML-EC model. The valence-electron correlation energies and reaction energies calculated using the constructed model were in good agreement with the reference values, the latter of which were superior in accuracy to density functional calculations using 71 exchange-correlation functionals. The numerical results indicate that the FCA is useful for constructing a versatile model.
机器学习电子关联（ML-EC）模型是一种密度泛函形式的回归模型，它基于波函数理论再现关联能量密度。在先前的一项研究中[T. Nudejima等人，《化学物理杂志》151, 024104 (2019)]，ML-EC模型是使用包含核心极化函数的基组进行全电子计算得到的关联能量密度构建的。在本研究中，我们对关联能量密度应用了冻结核心近似（FCA），以降低机器学习中使用的响应变量的计算成本。从基于网格的能量密度分析中获得的耦合簇单、双和微扰三激发[CCSD(T)]关联能量密度，在FCA和不含核心极化函数的关联一致基组内进行了分析。使用外推法和复合方案获得了关联能量密度的完全基组（CBS）极限。基于这些方案的CCSD(T)/CBS关联能量密度表现出合理的行为，表明其作为响应变量的适用性。正如预期的那样，计算时间显著减少，特别是对于包含大量内壳层电子元素的系统。基于密度与密度的关系，从30个分子中积累的大量数据（5662500个点）足以构建ML-EC模型。使用构建的模型计算的价电子关联能和反应能与参考值吻合良好，后者的精度优于使用71种交换关联泛函的密度泛函计算。数值结果表明，FCA对于构建通用模型很有用。
